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16 Cards in this Set
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Heron
1. Where from? 2. What were his two works called? 3. What did he find out? 
1. an Egyptian with Greek training
2. Geometric (problems on mensuration) and Mechanical (descriptsion of ingenious mechanical devices) 3. A method of finding a sqrt approximation of a nonsquare interger 

Heron's method of finding square root approximation.

If n=ab, then sqrt(n) is approximated by (a+b)/2, then the approximation improving with the closeness of a tob.
a(1) = first guess a(2) = [a(1)+n/a(1)]/2 a(3) = [a(2)+n/a(2)]/2 

Use Heron's method of sqrt approxmation to find the square root of 54.

7.35


What are the three stages in historical development of algebraic notation ?

1. Rhetorical Algebra
2. Synocopated Algebra 3. Symbolic Algebra 

Rhetorical Algebra

Solution of a problem written without abbreviations of symbols


Syncopated Algebra

Abbreviations are adopted for some of the more frequrently reoccuring quantities and operations


Symbolic Algebra

Solutions appear largely in a mathematical shorthand made up of symbols having little apparent connection with teh entities they represent.


Three works of Diophantus

1. Arithmetica
2. On Polygonal Numbers 3. Porisms 

Diophantine Problems

Intermediate algebraic problems in which one must find only the rational solutions


How do you solve a Diophantine Equation?

a is similar to b (mod m) if and only if a/m, b/m have the same remainder


What work did Ptolemy Soltec write?

"Almajest"


State Ptolmey's Theorem

In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the prodcuts of the two pairs of opposite sides


What is Ptolemy's method of square root?

Refer to book, pg 177


What are the two types of Liberal Arts?

1. Quadrivium
2. Trivium 

What are the four Quadrivium?

1. Arithmetic
2. Music 3. Geometry 4. Astronomy 

What are the Three Trivium?

1. Logic
2. Grammar 3. Rhetoric 